The group of joggers received only bumps and bruises, the Southeast Missourian reported Monday.
Vincent T. Anderson of Little Rock and Marcus E. Jones of Cotton Plant were arrested.
Police said the joggers were struck within 10 minutes after the car was reported stolen shortly before 7 a.m.
Officials have not released a possible motive for the attack, but Sgt. Brad Smith said the investigation indicates "it was a deliberate act."
Ron Rosati, provost at Southeast Missouri State University, was among the injured. He said the vehicle was stopped at an intersection as the joggers passed in front of it and the car accelerated across lanes to hit them.
Anderson, 19, has been charged with five felonies, including first-degree assault, tampering with a motor vehicle and resisting arrest. Jones, 27, the passenger, faces misdemeanor charges of second-degree vehicle tampering and resisting arrest.